( Reaffirmed 1998 ) IS : 5477 ( Part IV ) - 1971 Indi& Standard METHODS FOR FIXING THE CAPACITIES OF RESERVOIRS PART IV FLOOD STORAGE Catchment Area and Reservoirs Sectional Committee, BDC 48 ChIliWll~ +RI N. V. KEURSAL~ Members SEBI R. D. GU~TE ( Alternatr to Shri N. V. Khursale ) DIREO~OR Da S. R. SEHOAL ( .&mot# ) Central DIBEOTOR( HYDFCOLOQY ) SERI B. GA~UDACHAR ( Altemotr) `Drn~crron (INTERSTATE & DESICJN~ ) SHar P. V. RAO ( Afkmata) Sam D. DODDIAH SERI R. L. GU~TA SUPERINTENDINO ENQINEER ( DESIGNS) ( Akmnti ) SHRI S. N. GUPTA SHRI V. S. KRISHNASWAMY SRRI p. N. MALHOTRA `@RI R. N. HOON ( Altemte ) Central Boards of Irrigation Geological Bhakra Dams Organization, Damodh~n~~lley Pate1 Engineering & Power, New Delhi Nangal Township Maithon Dam, Survey of India, Lucknow Water & Power Commission, Department, New Delhi of Andhra Land Reclamation, Irrigation Institute, Amritsar St Power Research Irrigation Reflmmtinf Department, Government of Maharashtra Public Works Pradesh Government Public Works Department, PublgraWzhkr Department, Government Government of Mysore of Madhya SARI B. N. MURTEY &RI Y. G. PATEL SHRI H. R. PRAMANIK Corporation, Company Ltd, Bombay Department, Government Irrigation 8 Waterways of West Bengal ( Continuedon page 2 ) INDIAN MANAK. STANDARDS BHAVAN, 9 BAHADUR NEW DELHI INSTITUTXON SHAH llooO2 ZAFAR MARC IS: 5477 (Part IV) - 1971 ( ConrinusdJfom pug8 1) Representing Planning Commission, New Delhi NationnLiProjects Construction Corporation, New Members Da S. P. RAYOHAUDHTJRI SHRI P. SAM~ATH SHRI K. N. TANEJA (Altermats) Soil DR R. V. TAMHANE SERI BIJAYANARDA TIXIPATEY SHRI D. AJITRA SIYEA, Director ( Civ Engg ) Conservation Division ( Ministry of Food, Agriculture, Community Development & Cooperation ) , New Delhi Irriga;y= & Power Department, Government of Director General, IS1 ( Er-oJi& Mmbcr ) SHRI K. RAQHAVENDRAN Deputy &actor ( Civ Engg ), IS1 2 IS :5477 ( Part IV ) - 1971 Indian Standard METHODS FOR FIXING THE CAPACITIES OF -RESERVOIRS PART IV FLOOD STORAGE 0. FOREWORD 0.1 This Indian Standard (Part IV ) was adopted by the Indian Standards Institution on 19 February 1971, after the draft finalized by the Catchment Area and Reservoirs Sectional Committee had been approved by the Civi4 Engineering Division Council. 0.2 Flood storage depends on the height at which the maximum water level ( MWL ) is fixed above the normal conservation level ( NCL ). The determination of the MWL involves the routing of the design flood .through the reservoir and spillway. When the spillway capacity provided is low, the flood storage required for moderating a particular tlood will be large and vice versa. A higher MWI involves larger submergence and hence this aspect has also to be kept in view while fixing the MWL and the flood storage capacity of the reservoir. 0.3 This standard consists of four parts and the other parts are as follows: IS : 5477( Part I )- 1969 Methods for fixing the capacities of reservoirs: Part I General requirements IS:5477(Part II)-1969 Methods for fixing the capacities of reservoirs: Part II Dead storage IS:5477 (Part III)-1969 Methods voirs : Part III Live storage for fixing the capacities of reser- 0.4 For the purpose of deciding whether a particular requirement of this standard is complied with, the final value, observed or calculated, expressing the result of a test or analyL shall be roundedoff in accordance with The number of sl\rnificant places retained in the rounded off IS:2-1960*. value should be the same as that of the specified value in this standard. 1. SCOPE 1.1 This standard ( Part IV ) iovers the criteria and procedure to be followed in fixing the flood storage capacity of a reservoir consistent with the *Rules for rounding off numerical values ( revised ;. IS : 54r7 (paXfv ) - i97i itself and the life and properties downstream of the safety of the structure reservoir. 2. TERMINOLOGY 2.0 For the purpose of this standard, the following definitions shall apply. 2.1 Normal Conservation. Level (NGL) -The normal conservation level is the highest level of the reservoir at which water' is intended to be held for various uses other than flood control. 2.2 FUR Reservoir Level (FRL) - Is the highest level of the reservoir at which water is intended to be held for various uses including part or total of the flood storage without allowing any passage of water through the spillway. 2.3 Maximum Water Level ( MWL ) - Is the highest level to which the reservoir waters will rise while passing the design flood with the spillway facilities in full operation. 2.4 Surcharge Storage-The storage between the crest of an uncontrolled spillway or the top of the crest gates in normal closed position and the MWL is termed as the surcharge storage. 2.5 Maximum Probable Flood -1s the flood that may be expected from the most severe combination of critical meteorologic and hydrologic conditions that are reasonably possible in the region, and is computed by using the maximum probable storm which is an estimate of the physical upper limit to storm rainfall over the basin. This is obtained from storm studies of all the storms that have occurred over the region and maximizing them for the' most critical atmospheric conditions (see A-2.1.1 of Appendix A also). 2.6 Standard Project FloodIs the flood that may be expected from the most severe combination of meteorologic and hydrologic conditions considered reasonably characteristic of the legion and is computed from the standard project storm rainfall reasonably capable of occurrence over the basin in question and may be taken as the largest storm which has occurred in `the region of the basin during the period of weather record. It is not maximized for most critical atmospheric conditions but it may be transposed from an adjacent region to the water-shed under consideration. Is the flood adopted for design purposes. It may be 2.7 Design Floodthe maximum probable flood or the standard project flood or a flood corresponding to some desired frequency of occurrence depending upon the standard of security that should be provided against possible failure of the structure. 4 IS t 5477 ( Part IV ) - 1Sil 3. GENERAL 3.1 A prerequisite essential to the safety of the Adamis a decision in regard to the standard of security that should be provided against possible failure of the concerned structure during extraordinary floods. In case, failure of the structure is likely to result in loss of life or widespread property damage in addition to the damage of the structure itself as in the case of spillways of large reservoirs, a very high degree of security shall be provided against failure under the most severe flood conditions considered reasonably possible. But when loss of life is not involved, economic considerations would prevail to govern the selection of the design flood. would be filled to the full reservoir level at the beginning of the spillway design flood. Even though the contemplated plan of reservoir operation indicates that a portion of the storage capacity below the FRL probably would be available at the beginning of the spillway design flood, the possibility of improper operation of regulating outlets as the result of incorrect flood predictions, mechanical difficulties, plugging of conduits by debris, or negligent attendance may justify the assumption of a full reservoir at the beginning of the design flood. Moreover, future developments may require revisions in the original plan of reservoir operation or changes in the use of the reservoir that would increase the probability of a full reservoir at the beginning of the spillway design flood. 4. ESTIMATION OF DESIGN FLOOD 3.2 It should be assumed that the reservoir 4.1 The methods in vogue for estimation classified as under: of design flood are broadly a) Application of a suitable factor of safety to maximum ~observed flood or maximum historical flood, b) Empirical flood formulae, c) Envelope curves, d) Frequency analysis, and e) Rational method of derivation of design flood from storm studies and application of unit hydrograph principle. 4.2 Application of a Suitable Factor of Safety to Maximum Observed Flood or Maximum Historical Flood -The design flood is obtained by applying a safety factor which depends upon the judgement of the designer to the observed or estimated maximum historical flood at the project site or nearby site on the same stream. This method is limited by the highly subjective selection of a safety factor and the length ofavailable stream flow record which may give a quite inadequate sample of flood magnitudes likely to occur over a long period.of time. 5 Isi5477 (Part IV ) - 1971 Flood Formulae -The empirical formulae commonly used in the country are the Dicken's formula, Ryve's formula and Inglis' formula in which the peak flow is given as a fun,ction of the catchment area and a coefficient. The values of the coefficient vary within rather wide, limits and have to be selected on the basis of judgement. They have limited regional application, should be used with caution and only, when a more accurate method cannot be applied for lack of data. 4.3 Pmpirical 4.4 Envelope Carves -In the envelope curve method maximum flood is obtained from the envelope curve of all the observed maximum floods for a number of catchments in a homogeneous meteorological region plotted against drainage area. This method, although useful for generalizing the limits of floods actually experienced in the region under consideration, cannot be relied upon for estimating maximum probable floods for the determination of spillway capacity except as an aid to judgement. 4.5 Frequency Analysis -The frequency method involves the statistical analysis of observed data of a fairly long (at least 25 years ) period. 4.5.1 A purely statistical approach when applied to derive design floods for long recurrence intervals several times larger than the data has many limitations and hence this method has to be used with caution. 4.6 Rational Method of Derivation of Design Flood from Studies and Application of Unit Bydrograph Principle 4.6.1 The steps involved, in brief, are: Storm a) analysis of rainfall 7s run-off data for derivation of loss rates under critical conditions; b) derivation of unit hydrograph by analysis (or by synthesis, in cases where data are not available); c) derivation of the design storrir; and d) derivation of design flood from the design storm by the application of the rainfall excess increments to the unit hydrograph. Appendix A provides the criteria for estimation of design flood. 4.6.2 Unit Hydrograph -Limitations a) The unit hydrograph ~principle is not applicable for drainage basins having an area of more than 5 000 km2 where valley storage effects are not reflected and where variation of rainfall in space and time shows a tendency to become too great to be reflected in the unit hydrograph. b) Application of the unit hydrografih principle is also not recommended for catchments having an area less than about 25 kmz. 6 IS : 5477 ( Part IV ) - 1971 cl 4 Large number of raingauges suitably located should be available in. the entire catchment to reflect the true weighted rainfall of the catchment. Unit hydrograph principle is not applicable when appreciable proportions of the precipitation occurs in the form of snow or when snow covers a significant'part of the catchment. OF MAXIMUM WATER LEVEL 5. DETgRMINATION 5.1 The maximum water level of a reservoir is obtained by routing the design flood through the reservoir and spillway. This process of computing the reservoir stages, storage volumes and outflow rates corresponding to a particular hydrograph of inflow is commonly referred to as flood routing. The routing is determined by the following: a) Initial reservoir stage; b) The design-flood hydrograph ; c) Rate of outRow including the flow over the crest, through sluices or outlets and through power units; and d) Incremental storage capacity (each stage ). 5.1.1 Although there are definite relations -between reservoir inflow, storage, and outflow these relations are usually difficult to express algebraically. Therefore, a step-by-step computation procedure is followed whereby the increase in storage and rate of outflow resulting from the volumes of inflow during successive short increments of time are computed. Increments of inflow are computed for periods of time sufficiently short to warrant the assumption that the mean of the inflow rates and the mean of the outflow rates at the beginning and end of the intervals would closely approximate the average rates for the respective periods. 5.2 Appendix B provides an illustration with the details of routing the inAow hydrograph through a storage reservoir and fixing the maximum water level, Appendix C gives an example based on graphical ( Sorensen ) method of routing the inflow hydrograph through a reservoir. APPENDIX A ( Clauses 2.5 and 4.6.1 ) CRITERIA DAMS A-l. GENERAL A-l.1 Each site is individual causes and effects. Therefore, in its local conditions, and evaluation of only general guidelines are provided and 7 FOR ESTIMATION OF DESIGN FLOODS AND OTHER HYDRAULIC STRUCTURES FOR IS : 3477 ( Part IV ) - 1971 the hydrologists and the designer would have the discretion to vary the criteria in special cases, where the same are justifiable on account ofassessable and acceptable local conditions, which should be recorded and have the acceptance of the competent authority. A-2. DETERMINATION A-2.1 Major A-2.1.1 and Medium OF DESIGN Reservoirs FLOOD Maximum Probable Flood- In the design ofspillwaysfor major and medium reservoirs ( with storages more than 6000 hectare metres ) the maximum probable flood should be used. The maximum probable flood is estimated from the maximum probable storm applying the unit hydroThe maximum probable storm is an estimate of the graph principle. physical upper limit to storm rainfall over a basin. It is obtained from the studies of all the storms that have occurred in the region and maximizing them for possible moisture charge and for storm efficiency. The method of moisture adjustment commonly used involves the estimation of air moisture content from surface level dew point observations. Maximizing storm efficiency is achieved by storm transposition which assumes that the most effective combination ofstorm efficiency and inflow wind has either occurred or has been closely approached in the outstanding storm on record. Further adjustment of storm precipitation data to the estimated maximum sustained wind to carry this maximum moisture supply into the project basin is not attempted unless very high design safety factors are desired or only very limited storm rainfall data are available. A-2.1.2 Distribution of Storm Rainfall - The distribution of storm intensities for smalldurations is obtained on the basis of recorded data of selfrecording raingauge stations in the catchment or region. A-2.1.3 Maximization for Unit Hydrograph Peak- It is observed in practice that the unit hydrograph peak obtained from heavier rainfalls is about 25 to 50 percent higher than those obtained from the smaller rainfalls. Therefore, the unit hydrograph from the observed floods may have to be suitably maximized up to a limit of 50 percent depending upon the judgement of the hydrologist. In case the unit hydrograph is derived from very large floods, then the increase may be of a very small order; if it is derived from low floods the increase may have to be substantial. A-2.1.4 Loss Rate-The loss-rate should be estimated from the volume of observed flood run-off and the corresponding storm that caused the flood. A minimum loss rate should be worked out and adopted for computing the design blood. A-2.2 The probability method, when applied to derive design floods for long recurrence intervals several times larger than the length of data, has 8 IS: 5477 ( Part IV ) - 1971 many limitations. In certain case& however, like that of very large catchments where unit hydrograph method is not applicable and where suficient long term discharge data is available, the frequency method may be the only course possible. In such cases the design flood to be adopted for major structures should have a frequency of not less than once in 1000 years. Where annual flood values of adequate length are available, `they are to be analyzed by Gumbel's method (see Appendix D ), and where the tata is short, either partial duration method or regional frequency techniq,*e is to be adopted as a tentative approach and the results verified and cht-ked by hydrological approaches. Sometimes when the flood data is inadequate, frequency analysis of recorded storms is made and the storm of a particular frequency applied to the unit hydrograph to derive the flood; this flood usually, has a return period greater than that of the storm. A-2.3 Barrages and Minor Dams -In the case of parmanent barrages and minor dams with less than 6000 hectare metres storage, the standard project flood or a lO0 year flood,' whichever is higher, is to be adopted. A-2.3.1 For pick-up weirs a flood 50-100 years frequency should be adopted according to its importance, and level conditions. A-3. PROVIS'ONS FOR OTHER.FACTORS A-3.1 The initial reservoir level before the impact of the spillway design flood has to be taken as at, full reservoir level. In regions experiencing prolonged floods where storms in quick succession are experienced, the spillway may also be checked for design flood preceded or succeeded by a The interval between these two flood of once in 25 years frequency. floods ( peak to peak) may be taken as 3 or 5 days according to as the region lies in an annual rainfall zone of more than 100 cm or less than 100 cm respectively. A-3.2 To provide for mechanical and other failures, it is assumed that some gates as inoperative with a maximum of 10 percent and a minimum of one gate. For this purpose the designer may be permitted to increase permissible stresses treating it as an extraordinary occurrence, like earthquake. APPENDIX ( Clause 5.2 ) B STEP-BY-STEP METHOD OF RESERVOIR FLOOD ROUTING FOR FIXING MAXIMUM WATER LEVEL ( MODIFIED PULS' METHOD ) B-l. BASIC DATA REQUIRED B-l.1 The following is the basic data: (see Fig. 1 ), a) Reservoir level MYSUSspillway capacity (outflow) and storage capacity (see Fig. 1 )i 9 1s : 5477 ( Part IV ) - 1971 b) Full reservoir level; c) Inflow hydrograph (see Fig. 2 ); d) Initial outflow; and e) Initial storage (or initial reservoir level). I I I J 394.51' - 1 O.&a 0.50 o-60 0-70 040 040 STORAGE ( h8.m xl 8 ) 5000 10000 14oeo 2oooo OUTFLOW bf?/s) zsow FIG. 1 RESERVOIR LEVELS Vs SPILLWAY AND STORAGE CAPACITIES 399-o 2 u-l 398-O 28 397.0 5 Q 396.0 9 z 2 395.0 396.0 393.0 TIME IN HOURS FXG. 2 TNFI.OW AND OUTFLOW HYDROCRAPHS, AND TIME J's RESERVOIR LEVELS FOR THE DESIGN FLOOD HYDROGRAPH 10 IS-:5477 ( Part IV ) - 1971 B-2. BASIC EQUATION RESERVOIR FOR ROUTING FLOOD THROUGH B-2.1 Basic equation for routing flood through reservoir is given below: t(qA)_t(s+2q where t = time interval, 11 = initial inflow in ma/s, =s,-s,=*s , (1) I.. 1s = final inflow in ma/safter t h, Ot = initial outflow in ma/s, 0 s = final outflow in msjs after t h, S, = final gross storage in cumec h after t h, S, = initial gross storage in cumec h, and n.9 = incremental storage in time t h. Storage capacity is usually given in hectaremetres which should be converted into cumec h or cumec day, if the time interval t is expressed in hours or a part of a day. B-3. PROCEDURE w3.1 Taking known values on one side (A+) S ha.m sha.m f + ($2) =2.771 ~2.771 S cumec h = (;t+;) ......... ... ... ...... ... . . . (2) (3) (4) . . . (5) 1 cumec day = 24 cumec h = 8.64 ha-m S/t cumec h Taking the time interval t as 6 h S t =0.463 S ... 1 is prepared. 1, Fig. 3 is prepared. 1-l ... ... . . . (6) B-3.2 From Fig. 1, Table B-3.3 By means of Table IS : 5477 ( Part IV ) - 1971 TABLE 1 RESERVOIR LEVEL k's $ + -$ ) ( ROUTING PERIOD ( Clause i-3.2 - 6 HOURS ) RESERVOIR LEVEL m) STORAGE (S) S =Oa463s OuTFLoW (ha.a.X106) t (cumecx lOa) (3) 0.222 3 O-257 7 0.297 0 0.340 5 (cumec x 1O8) (4) 0.005 5 0007 3 0.008 9 0.011 1 (cumec X lo@) (cumecX 10') (5) 0.002'8 0.003 I 0.004 5 0.005 6 (6) 0.225 1 0.261 4 0.301 5 0.346 1 ' o/2 (`1 394.8 396.3 397.8 399.3 (2) 0.480 0 0.556 5 0,641 3 0.735 3 B-3.4 Referring to Table 2, co1 1 and 2 are inflow hydrograph (Fig. 2 ). The values given of successive inflows. Column 4 is obtained by value from the initial S/t value ( which is either Fig. 1 knowing the initial reservoir level). Column Column 5 is the sum of co1 3 and 4. 6 is obtained by referring obtained from the given in co1 3 are the average subtracting the initial 012 known or read out from to Fig. 3 for the values ofco15. and the Corresponding to the values of co1 6, the values in co1 7 are obtained by referring to Fig. 1. With the values given in co1 6 and 7, the outflow hydrograph curve of reservoir level with time are drawn in Fig. 2. FIG. 3 $ + -& Vs OUTFLOW CURVE 12 IS : 5477 ( Part IV) - 1971 TABLE 2 ROUTING OF DESIGN FLOOD THROUGH ( ROUTLNG PERIOD - 6 HOURS ) ( Clause B-3.4 ) RESERVOIR TIME h INFLOW d/s x 1oa m (2) (1) 26 32 38 44 50 (3) 0.009 7 (4) 0,252 3 (5) O-261 4 0.262 0 (6) 0.007 1 0.007 3 0.007 6 0.008 1 0.008 6 0.009 1 0.009 5 O-009 6 0.009 6 0.009 4 0.009 1 0.008 8 0.008 4 0.008 0 0.007 7 3.007 4 O-007 1 (7) 396.30 FRL 396.42 -39676 397.14 397.59 397.98 398.2 1 398.3 1MWL 398.28 398.19 397.98 397.67 397-43 397.09 396.79 396.58 396.22 O-007 1 0.012 3 0.014 7 0.017, 1 0.018 2 0.019 3 0.019 4 0.019 6 0.018 9 0'018 2 0016 5 0.291 9 0.282 2 0.271 4 O-261 5 0.254 7 O-269 4 0.279 7 O-290 8 o-301 1 52 68 74 80 86 92 98 104 110 116 122 0.014 9 0.013 0 o-011 0 0.009 2 o-007 4 0.005 7 0.004 1 0.003 2 0.002 3 0.001 7 O*OOl1 0~000 9 OaKI 6 0.000 6 O-000 5 o*ooo 5 OaO 4 0.000 4 o*oOO4 OaOO 4 o&O 4 0'256 4 0~263.0 0.270 3 0.277 7 0.285 2 0.289 5 0.298 4 0.302 1 O-302 4 o-299 0 0.308 4 0.312 0 O-311 6 0.307 8 O-301 6 0.291 3 0.286 1 O-278 3 01270 8 O-265 4 0.256 8 13 IS : 5477 ( Part IV ) - 1971 APPENDIX ( C&se 5.2) C OF RESERVOIR MAXIMUM GRAPHICAL (SORENSEN'S) METHOD FLOOD ROUTING FOR FIXING WATER LEVEL C-l. C-l.1 BASIC DATA REQUIRED The following is the basic data: a) Reservoir level zwsus spillway capacity and storage capacity (see Fig. 4 ); b) Full reservoir level; c) Inflow hydrograph (see Fig. 5A); d) Initial outflow; and e) Initial storage (or initial reservoir level). (outflow) (see Fig. 4), C-2. BASIC EQUATION RESERVOIR d,.Y= (Z-O) where df FOR ROUTING FLOOD THROUGH C-2.1 Basic equation for routing flood through reservoir is given below: . .. ... ... . ..(7) dS = change in reservoir storage, Z= rate of inflow, 0 = spillway discharge rate (or outflow rate \, and dt = time interval. As the inflow is a function of time and outflow is a function of storage, equation (7) may be written as: s= Sf - sj = [ i _ L!?-tOI)_ at 2 where 7 is the average inflow for the period At and the subscripts `i' and `f' refer to the initial and final conditions of the period at. C-3. PROCEDURE C-3.1 For graphical solution, equation (8) is transposed as follows: 1 ... (si+ y) + (i-oi ) at=s,+o,-y 14 . ..(9) IS : 5477, ( Part Iv ) - 1971 239.25 I l-25 1 I I I I 4 2.50 0.25 3.75 0.50. 5.00 0.75 (SISTORAGE .~. 6.25 (1000 ha.m) l-00 ha.m PER 7.50 1.25 h) 6.75 l*ko 0 FIG. 4 L (O)OUTFLOW(lOOO RESERVOIR LEV-EL Vs STORAGE AND OUTFLOW CURVES value of A t is selected, A constant inflow hydrograph (here A t = 1 h ). on the shape of the OAt are plotted The values of S + - 2 in Fig. 5B, and (b) spillway depending as a function of (a) reservoir level as shown discharge (or outflow ) ps shown in Fig. 5C. NOTE -The OAt 2 scales for the ordinates ofFig. 5A and 5C should be the same. versus outflow In Fig. 5C by the side of S + curve, a line A is C is the drawn with the same origin such that its slope is --&- where OAt ratio Of S + -scale to the Y-axis o?Fig. to the 0 scale ( that iqratio 5C ). 15 of the scale of X-axis IS : 5477 ( Part IV ) - 1971 1 250 ratio works out to 250= For this particular example, A t is taken as one hour and the scale 5, which determines the slope of the line A. At 0800 h the reservoir inflow and the outflow are known. To determine the reservoir level one hour later, that is at 0900 h, the following procedure is adopted: 4 b) Draw a horizontal line a from the value of the average inflow 7 for the period 0800 h to 0900 h, towards Fig. 5C. Draw a line b in Fig. 5C parallel to line A, from the intersection of horizontal (towards Kg. 5C) corresponding to the initial outOAt flow at 0800 h and the curve of S + 2 versus 0 in Fig. 5C. intersection point of lines a and b is projected Fig. 5B and 5C to get the points Yand Xrespectively. The point Y of Fig. 5B is projected horizontally the reservoir elevation at 0900 h. vertically in The c> 4 4 to Fig. 5D to get The point X of Fig. 5C is projected horizontally to Fig. 5A to get the outflow 0, at 0900 h. new reservoir level and outflow values as initial conditions the steps a to e are repeated for the next hourly increment. Thus reservoir stage hydrograph Fig. 5D and the outflow hydrograph Fig. 5A ( superimposed on the inflow hydrograph) are obtained. f 1 With The curves of Fig. 4 are not directly involved in the graphical solution but are~the basic data for plotting Fig. 58 and 5C (see Table 3). TABLE 3 COMPUTATION ( WITH STORAQE, OF VALUES FOR AI AS 1 HOUR ) OUTFLOW, O1000 ha. m/h l&g. 5B AND 5C ELEVATION m S 1 000 ha. m OAt - 2 I 000 ha. m (4) 0.016 0.060 0.100 o-151 0.306 0,494 s+ OAt 2- 1 000 ha. m (5) 1'516 2.160 2.600 3.388 -5494 7.994 L (1) 240.70 242.25 243.02 243.80 245.35 246.90 (2) I.500 2*100 2.500 3'237 5.188 7,500 (3) 0,032 0,120 0.200 0,302 O-612 0.987 16 As in the Original Standard, this Page is Intentionally Left Blank IS : 5477 ( Part IV ) - 1971 APPENDIX D (Clausi A-2.2 ) ESTIMATION OF PARAMETERS OF GUMBEL'S EXTREME VALUE DISTRIBUTION AND DETERMINATION OF PEAK FLOW OF LONG TERM RETURN PERIOD D-l. D-l.1 MAGNITUDE PERIOD Gumbel F(x)& OF PEAK FLOW OF A GIVEN RETURN postulated = ae-+-u)e-e the use of extreme -a(%-U) dx value distribution ... . ..(iO) peak where a and u are to be evaluated from n years annual observed .`..........".......) xn. flow values xl, x2, x3 ,............"......... Peak floy magnitude XT of T years return period is evaluated from XT = u - (l/a) =u-- log, loge T/( T - 1 ) 2.302 6 -- l0.362 3 + logro log10 -T_ u , D-2. EXAMPLE D-2-1 A worked out example as given in ( 1 ma/s `= 1000 Referring Table l/s ). to Table 4, 4 1 ;..(ll) for data of Sabarmati at Dharoi illustrates the computational ( 1935 - 52 ), procedure mean flood =z Standard $= = = --g$.= L$? = 98.352 g ... . ..( 12) deviation 2` (x-ZJB n-l 256 002 - s is given by 2x8 - (Z X)" n L 5 ,22.242 650 ... . ..( 13) 164446.11;6- :. s = 75.645 50Q6 to a, take Computation for `a' As a first approximation al =Fr x _+= 0.016955 . . . . ..( 14) Then co1 5 in Table 4 is completed. For an, as, ar, etc, of co1 6, 7 and 8 of Table 4, a step-by-step method of computing successive approximations ak + 1 from ak is given in Table 5, which is self-explanatory. Successive approximations are continued in Tables 4 and 5 till a negligibly small `value approaching 0 of hk is reached in Table 5. 19 . fSr5477(PareIV)-1971 TABLE 4 VALUE OF c-az ( Clause D-2.1 ) PEAK FLOW RATE (x) `:;y I -a,p YEAR ,-V e ,-v -laoa 4 (1) (2) 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1951 1952 TOTAL (3) 76 ld 2:; 91 :s 193 246 187 z 20 48 102 6 1672 (4) 5 776 15 62: 6 241 51 529 8 281 1 764 15 625 37 249 60 516 34 969 2 025 3 249 2% 10 404 36 256 002 (5) 0.275 0.950 0.120 0.262 0.021 0,213 0.490 0.120 0.037 o-015 0.042 0466 0.380 0.712 0.443 0.177 0.903 7 4 1 0 3 7 6 1 9 4 0 2 5 4 2 4 3 (6) 0.263 1 0948 6 0.1113 0.249 7 0.018 6 0.202 2 0.478 2 0.111 3 0033 7 0.013 3 0.037 5 0.453 6 0,367 5 0.703 7 0.430 3 0.166 6 0.899 9 5489 1 (7) 0262 0.948 0.110 0249 0.018 0.201 0.477 0.110 0.033 0.013 0.037 0.452 0.366 0.703 0429 0.166 0,899 4 6 8 0 4 6 4 8 5 2 2 9 7 3 6 1 7 (8) 0262 0.948 0.110 0.249 0018 0.201 0.477 0.110 0033 @013 0.037 0'452 0366 0.703 C.429 0.166 0899 4 6 8 0 4 5 4 8 5 2 2 9 7 3 6 I 7 5.632 2 54812 5.481 1 ,Computation for `IO From the steady case ), compute u= value so reached of ak for k = 4 (in the present logslOX 64.297 -$ 104 C log10 (n)--loglo (Ze -akzi ) = 1 . ..( 15) Putting these values of I( and the steady ok in ( 11 ), expected peak values %r for T = 50; 100; 200; 500, etc, years return periods are evaluated as ~6s = 285.97; In order xlw = 325.63; xzoo= 365.15; ~500 = 417.30 from small samples of 29, 30, ..`.......... . incidental errors of estimation arising _., years observed data available the above best estimates may be increased by I.645 SE(xr ) to warrant 95 percent dependability of the design estimates. The standard error of 20 to safeguard against IS : 5477 (Part IV ) - 1971 estimation $E( XT ) is given by a :-;;-[I --log, SE( XT ) = + -$-{ loger/(z--1) l-O.577216 ... . ..(16) 1 = ___ a&- [ 1 + 0.607 927 1 ... . ..(17) -log,logeT/(2--1) Thus x60-= 2 859 700 3 651 500 l/s ( = 2 859.7 ,, ( = 3 256.3 ,, ( = 3 651.5 ma/s) + 797.3 ms/s ma/s) + 916.1 ms/s) + 1035.7 ma/s ms/s x100 = 3 256 300 xzoo = xsoo = 4 173 000 ,, ( = 4 173.0 ma/s) + 1 194.6 ma/s Values of A = --log, loge T/( T1 ) for the most commonly used values of T like 20, 50, 100, 200,50@,.and 1000 years are reproduced below for convenience of users: l-=20 A ~2-9702 50 3.9020, 100 4.6002 200 5.2958 500 6.2137 1000 6.9073 D-2.2 It is advisable and not to compute 2% years. to procure always at least 20-25 years observed records estimates for return periods longer than about 20n or D-2.3 The steps remain very much the same irrespective of the value of n, the number of years. Though the computational steps by successive approximation method appear very arduous, their schematically outlined procedure as in D-2.1, even with recorded data of around 50 years should not take a person equipped with an ordinary calculating machine and a book of logarithm tables more than 6-7 hours. With electronic fast computers the stabilized expression can be secured in two to three minutes for which programme is given in D-3. D-2.4 The calculation of a 500 years ' flood, for example does not tell when the flood is coming; it might occur in any year within that period or not until 500 years have elapsed. D-2.5 The choice of a suitable return period on which to base the `design flood' is the engineer's responsibility, and rests ultimately on his judgement and experience. The size and cost of the dam, the design freeboard, the amount of water stored, and the likely consequences of failure are factors which influence the selection. 21 TAlriLE 5 FOR VALUES OF @k + I &?koht #k ( Clause D-2.1 ) STEP QVANRTY k=l 0.016 955 0.007 363 58.979 6 3 478.593 2 39.373 3 k-2 0.017 565 0'007 628 56.931 4 3 241.184 3 41.421 5 5489 1 228.368 4 18 563.741 2 lflOl644 -26 895.564 3 -26 k=3 0.017 602 0+07 644 56.811 7 3 227.569 3 41.541 2 54812 227.711 1 18 488.027 9 oa15 475 719588 4 -26 k=4 0.017 602 58 0*007 645 56.809 9 3 227.364 7 41.543 0 54811 227.702 0 18 487.199 8 Of@0 663 717.284 3 b 2 6 5.632 2 7 8 9 10 f z Xi6 - =tic - 240.075 2 19 898.861 8 (5) (6) -30 18.316 900 038++15 z 2`8 f' wd (0,) = (7) - bk) = (8) + (5) (7) - (4) (6) 11 12 0.000 610 omo 037 Of)00 000 58 0.017 602 58 0.000 000 02 0.176 026 0 01: + , = ok + hk I 0.017 565 0.017 602 IS : 5477 (Part D-3. COMPUTER PROGRAMME FOR PEAK FLOOD TION BY MAXIMUM LIKELIHOOD METHOD IV) - 1971 ESTIMA- FIRST DATA CARD IS NO. OF OBSERVATION 4COLS, NAMES OF RIVER, SITE, UNIT OF OBSERVATION 8COLS EACH FOLLOWED BY DATA CARDS 4COLS EACH OBSERVATION. ~;~E~;ION X( 100 ), EX( 100 ) SQS&O. READ 2, N, RVR, SITE, UNIT 2 FORMAT ( 14,3A8) READ3, ( X (I), I=l, N ) 3 FORMAT (20F4.2) D05I=I,N SUM=SUM+X(I) 5 ;QS$M=SQSUM+X(I)**2 SQSUM=(SQSUM-SUM*SUM/B)/(B-1.) SUM=SUM/B T=3.141592654 &%;/SQRTF(6.*SQSUM) DO i.j=l, SIG=O. XSIG=O. XZSIG=O. A=A-H 20 -tiO-8 I=l, N EX( I ) =EXPF(-A*X(I)) SIG=SIG+EX(I) XSIG = XSIG + X( I )*EXf I 1 XZSIG = X2SIG + Xc'1 )*X( f)*EX( I ) FA = XSlG - ( SUM - 1./A )*SIG FH = ( SUM - 1,/A )fXSIG - XZSIG - SIG/A**2 H = FA/FH l.E - 06 ) 30, 30, 1 IF(ABSF(H)CONTINUE 30 ;I: T ;A/( T**2 ) U= T*LoGF( B/sxG ) X20 = U + T*2.970186 X50 = U + T*3.901953 xl00 = U`+ T*4.600150 X2nO = U + T*5.295775 X500 = U + T*6.213675 t' c l./( A*SQRTF (B ) ) SEX20 = P*SQRTF ( 1. + PIE*( 0.422784 SEX50 = P*SQRTF ( 1. + PIE*( 0.422784 SEX100 = P*SQRTF ( 1. + PIE*( 0.422784 SEX200 = P*SQRTF ( 1. + PIE*( 0.422784 SEX500 = P*SQRTF ( 1. + PIE*( 0.422784 PRINT 310, UNIT, RVR, SITE + 2.970186)**2 ) + 3.901953 )**2 ) + 4.600150)**2) + 5.295775 )**2 ) + 6.213675 )**2 ) 23 IS:%77 310 309 (Part IV)-1971 WITH VARIOUS RETURN Pm101 IIX, 9H2( FORMAT(IH1/////30X 43HEXPECTEDVALUES 1 46X, IH*, A8, 4X, lH*//4OX, A8,3X,2HAT,A8) PRlNT FORMAT( //29X. 8H20 YEARS, 12X, 8H50 YEARS, 11X, 9HlOO YEARS, 1 EARS, 11X, 9H500 YEARS) PRINT 311, X20, X50, X100, X200, X500 FORMAT( 8X. SHESTIMATE -, 5 ( 4X. F16.9 ) ) 311 PRINT 312, SEXBO, SEX50, SEXlOO, SEX200. SEX500 FORMAT( /9X, 8HSTD ERR =, 5 ( 4-X, F16.9 ) ) 312 STOP END _ _--_. _ !-4W __I 24